Let's start by drawing a diagram corresponding to the situation. Notice that the sushi roll can be modeled by a circle, with the chopsticks being .
The diameter of the circle is then 3.5 cm, the length of arc BC is 4.7 cm, and we are interested in the measure of angle ∠A. To find this, we'll first need the BC, which we can find by the . The circumference is
πd=π⋅3.5≈11.0 cm.
We can now calculate the arc measure.
circumferencearc length=360∘arc measure 11.04.7=360∘arc measure 11.04.7⋅360∘=arc measure 153.81818…∘=arc measure 154∘≈arc measure arc measure≈154∘
We now know that the measure of arc BC is 154∘. As ABOC is a quadrilateral, it has the interior angle sum 360∘. With m∠B and m∠C being 90∘, the sum of m∠A and m∠O must then be 180∘.
m∠A+m∠O=180∘ m∠A+154∘=180∘ m∠A=26∘
The measure of the circumscribed angle is 26∘.